Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories.

Andreas Irmler,Alejandro Gallo,Felix Hummel,Andreas Grüneis

doi:10.1103/physrevlett.123.156401

Abstract

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by 2 orders of magnitude without compromising accuracy.

Highlights

Introduction.—The ongoing advancement of modern electronic structure theories over the past few decades led to a proliferation of computational studies on atoms, molecules, and condensed matter systems based on first principles
Theory.—In this work we introduce a decomposition of the electronic transition pair correlation function and the corresponding correlation energy contributions
In passing we note that gdriverðr12Þ of a single electron pair can be well approximated in the complete basis set (CBS) limit at short interelectronic distances using a Slater-type correlation function, −γ−1e−γjr12j, where γ is a parameter that increases with increasing density [23]

Summary

Introduction

Introduction.—The ongoing advancement of modern electronic structure theories over the past few decades led to a proliferation of computational studies on atoms, molecules, and condensed matter systems based on first principles. In passing we note that gdriverðr12Þ of a single electron pair can be well approximated in the complete basis set (CBS) limit at short interelectronic distances using a Slater-type correlation function, −γ−1e−γjr12j, where γ is a parameter that increases with increasing density [23].

Results

Conclusion